Analysis of an atomistic model for anti-plane fracture

We develop a model for an anti-plane crack defect posed on a square lattice under an interatomic pair-potential with nearest-neighbour interactions. In particular, we establish existence, local uniqueness and stability of solutions for small loading parameters and further prove qualitatively sharp far-field decay estimates. The latter requires establishing decay estimates for the corresponding lattice Green's function, which are of independent interest

Polynomial Approximation of Symmetric Functions

We study the polynomial approximation of symmetric multivariate functions and of multi-set functions. Specifically, we consider $f(x_1, \dots, x_N)$, where $x_i \in \mathbb{R}^d$, and $f$ is invariant under permutations of its $N$ arguments. We demonstrate how these symmetries can be exploited to improve the cost versus error ratio in a polynomial approximation of the function $f$, and in particular study the dependence of that ratio on $d, N$ and the polynomial degree. These results are then used to construct approximations and prove approximation rates for functions defined on multi-sets where $N$ becomes a parameter of the input

Online Spatio-Temporal Learning with Target Projection

Recurrent neural networks trained with the backpropagation through time (BPTT) algorithm have led to astounding successes in various temporal tasks. However, BPTT introduces severe limitations, such as the requirement to propagate information backwards through time, the weight symmetry requirement, as well as update-locking in space and time. These problems become roadblocks for AI systems where online training capabilities are vital. Recently, researchers have developed biologically-inspired training algorithms, addressing a subset of those problems. In this work, we propose a novel learning algorithm called online spatio-temporal learning with target projection (OSTTP) that resolves all aforementioned issues of BPTT. In particular, OSTTP equips a network with the capability to simultaneously process and learn from new incoming data, alleviating the weight symmetry and update-locking problems. We evaluate OSTTP on two temporal tasks, showcasing competitive performance compared to BPTT. Moreover, we present a proof-of-concept implementation of OSTTP on a memristive neuromorphic hardware system, demonstrating its versatility and applicability to resource-constrained AI devices.Comment: Accepted at AICAS 202

Control of inherited structures and mechanical heterogeneities on the internal deformation of the Dolomites Indenter, eastern Southern Alps: a multi-scale analogue modelling study

During the Cenozoic evolution of the Alps, the Adriatic plate is traditionally considered as a rigid indenter. The structure of the northernmost part of the Adriatic plate in the eastern Southern Alps of Italy and Slovenia, referred to as Dolomites Indenter (DI), however, demonstrates significant internal deformation. Mostly Miocene shortening is accommodated within a WSW-ENE striking, S-vergent fold-and-thrust belt overprinting a pre-existing platform-basin geometry related to Jurassic extension. In this contribution we present two new sets of physical analogue experiments, addressing the effect of lateral crustal heterogeneities on the internal deformation of the DI on crustal- and lithospheric scale. The upper crust of the western Trento platform (western DI) is compositionally heterogeneous linked to Permian intrusives and extrusives (i.e., Athesian Volcanic Complex). Together with inherited basement structures this lateral heterogeneity, which strengthened the platform locally, is key for understanding upper crustal deformation and surface uplift patterns associated with Miocene basin inversion. We present brittle crustal-scale analogue experiments with inversion of pre-scribed platform-basin geometries, which indicate that variations in thickness, shape, and basement structure of especially the western platform (WP) have impact on timing and uplift of the DI’s upper crust. The mentioned variations in crustal composition, lead, compared to the reference model with simple platform-basin geometry, to (i) overall fewer thrust sheets, (ii) footwall cut-offs of the frontal thrust further in the hinterland, and to (iii) longer and flatter flats of the frontal thrust. Regarding the topographic evolution, a variation in, e.g., basement structure shows strain localization at the margin of the basal plate and stronger uplift within the southern part of the WP compared to limited uplift of the northern WP, which is consistent with documented little vertical movement north of the Valsugana fault system since the Jurassic. On the scale of the lithosphere, new analogue experiments with pre-scribed platform and basin geometries in the upper crust show similar lateral variations in thrust fault orientation across transfer zones as crustal-scale analogue models (Sieberer et al., 2023). Additionally, lateral variability of ductile lower crustal thickness predicts stronger uplift in areas of thicker lower crust. Documented thickening of the lower crust in some parts of the Southern Alps close to areas of higher uplift, tentatively interpreted being Miocene in age (Jozi Najafabadi et al., 2022), might support this finding. Ultimately our crustal and lithosphere-scale modelling predictions will be validated by high resolution low-temperature thermochronological data which cover the entire Dolomites Indenter

Feature-assisted interactive geometry reconstruction in 3D point clouds using incremental region growing

Reconstructing geometric shapes from point clouds is a common task that is often accomplished by experts manually modeling geometries in CAD-capable software. State-of-the-art workflows based on fully automatic geometry extraction are limited by point cloud density and memory constraints, and require pre- and post-processing by the user. In this work, we present a framework for interactive, user-driven, feature-assisted geometry reconstruction from arbitrarily sized point clouds. Based on seeded region-growing point cloud segmentation, the user interactively extracts planar pieces of geometry and utilizes contextual suggestions to point out plane surfaces, normal and tangential directions, and edges and corners. We implement a set of feature-assisted tools for high-precision modeling tasks in architecture and urban surveying scenarios, enabling instant-feedback interactive point cloud manipulation on large-scale data collected from real-world building interiors and facades. We evaluate our results through systematic measurement of the reconstruction accuracy, and interviews with domain experts who deploy our framework in a commercial setting and give both structured and subjective feedback.Comment: 13 pages, submitted to Computers & Graphics Journa